I need help with quadratics and indicies?

I was really confused about this one because of the 2y2
at the end instead of a number so I ended up with this:

= (x + 2y2)2 - (xy - 2y2)

Because

x2+ 4xy + 4y2 - xy - 2y2

= x2 + 3xy + 2y2

But it's not properly factoried so I'm unsure about it?

The next one was factorise: 4x2+ 2x + 1

I'm confused because
1 and 1 = 2 and 2 (*2) = 4 or 0 - not 2
4 and 1 (*4 and *1) = 5 or 3 - also not 2
and neither of these combinations work so I don't know what else to do?

And the last one is solve: (1/49)-1/2

I know that it means square root of 1/1/7 because the power1/2 = square root and the - means 1 over but 1/1/7 isn't a rational number and when I try turning it into a decemal it goes on forever and because it would be 1/0.143 (rounded) its still not a rational number so I am incredibly confused and would really apreciate help..? By the way I'm not aloud to use a calculator so could you please explain without one?

Re: I need help with quadratics and indicies?

I was really confused about this one because of the 2y2
at the end instead of a number so I ended up with this:

= (x + 2y2)2 - (xy - 2y2)

Because

x2+ 4xy + 4y2 - xy - 2y2

= x2 + 3xy + 2y2

But it's not properly factoried so I'm unsure about it?

The next one was factorise: 4x2+ 2x + 1

I'm confused because
1 and 1 = 2 and 2 (*2) = 4 or 0 - not 2
4 and 1 (*4 and *1) = 5 or 3 - also not 2
and neither of these combinations work so I don't know what else to do?

And the last one is solve: (1/49)-1/2

I know that it means square root of 1/1/7 because the power1/2 = square root and the - means 1 over but 1/1/7 isn't a rational number and when I try turning it into a decemal it goes on forever and because it would be 1/0.143 (rounded) its still not a rational number so I am incredibly confused and would really apreciate help..? By the way I'm not aloud to use a calculator so could you please explain without one?

If in doubt, you can always complete the square on one of the variables...

Re: I need help with quadratics and indicies?

I was really confused about this one because of the 2y2
at the end instead of a number so I ended up with this:

= (x + 2y2)2 - (xy - 2y2)

You should have (x+ 2y)2 as he first term. Squaring y2 will give you y4 that you don't want.

Because

x2+ 4xy + 4y2 - xy - 2y2

= x2 + 3xy + 2y2

But it's not properly factoried so I'm unsure about it?

The next one was factorise: 4x2+ 2x + 1

I'm confused because
1 and 1 = 2 and 2 (*2) = 4 or 0 - not 2
4 and 1 (*4 and *1) = 5 or 3 - also not 2
and neither of these combinations work so I don't know what else to do?

And the last one is solve: (1/49)-1/2

I know that it means square root of 1/1/7 because the power1/2 = square root and the - means 1 over but 1/1/7 isn't a rational number and when I try turning it into a decemal it goes on forever and because it would be 1/0.143 (rounded) its still not a rational number so I am incredibly confused and would really apreciate help..? By the way I'm not aloud to use a calculator so could you please explain without one?

Re: I need help with quadratics and indicies?

I was really confused about this one because of the 2y2
at the end instead of a number so I ended up with this:

= (x + 2y2)2 - (xy - 2y2)

Because

x2+ 4xy + 4y2 - xy - 2y2

= x2 + 3xy + 2y2

But it's not properly factoried so I'm unsure about it?

The next one was factorise: 4x2+ 2x + 1

I'm confused because
1 and 1 = 2 and 2 (*2) = 4 or 0 - not 2
4 and 1 (*4 and *1) = 5 or 3 - also not 2
and neither of these combinations work so I don't know what else to do?

And the last one is solve: (1/49)-1/2

I know that it means square root of 1/1/7 because the power1/2 = square root and the - means 1 over but 1/1/7 isn't a rational number and when I try turning it into a decemal it goes on forever and because it would be 1/0.143 (rounded) its still not a rational number so I am incredibly confused and would really apreciate help..? By the way I'm not aloud to use a calculator so could you please explain without one?

does not factorise over the reals (though it does over the complex numbers). Checking the discriminant will prove this.

Re: I need help with quadratics and indicies?

Originally Posted by Tabitha

And the last one is solve: (1/49)-1/2

I know that it means square root of 1/1/7 because the power1/2 = square root and the - means 1 over but 1/1/7 isn't a rational number and when I try turning it into a decemal it goes on forever and because it would be 1/0.143 (rounded) its still not a rational number so I am incredibly confused and would really apreciate help..? By the way I'm not aloud to use a calculator so could you please explain without one?

Two things that ought to help you out:

and

To get you started...

Can you finish from here? (By the way, you did get the answer: which is the correct answer.

Re: I need help with quadratics and indicies?

I'm sorry I've just clicked to that, so saying 1/1/7 would be the same as just saying 1 * 7, just like saying 1*1/7 is the same as saying 1/7.. That makes so much sence I just didn't click lol, thank you so much

Re: I need help with quadratics and indicies?

Originally Posted by Tabitha

I'm sorry I've just clicked to that, so saying 1/1/7 would be the same as just saying 1 * 7, just like saying 1*1/7 is the same as saying 1/7.. That makes so much sence I just didn't click lol, thank you so much